# Manjit Kumar

#### Quite Easily Done

### The Infinity Puzzle: How the quest to understand quantum field theory led to extraordinary science, high politics, and the world’s most expensive experiment

## By Frank Close

##### Oxford University Press 399pp £16.99 order from our bookshop

‘A desk or table, a chair, paper and pencils,’ was what Einstein asked for in 1933 when he arrived at the Institute for Advanced Study in Princeton. Then he remembered one last item: ‘Oh yes, and a large wastebasket, so I can throw away all my mistakes.’ In the next two decades before his death in 1955 there were plenty of them, but Einstein had earned the right to make those mistakes in search of his holy grail – a unified field theory.

In 1864 the Scottish physicist James Clerk Maxwell showed that electricity and magnetism were different manifestations of the same underlying phenomenon – electromagnetism. His great achievement was to encapsulate the disparate behaviour of electricity and magnetism into a set of four elegant mathematical equations that were to be the crowning glory of nineteenth-century physics.

Einstein sought a single, all-encompassing theoretical structure that would unify electromagnetism with his theory of gravity, the general theory of relativity. Such a unification was the logical next step for Einstein, but few were convinced, for in the twentieth century two new forces were discovered and given names that alluded to their strengths relative to the electromagnetic: the so-called strong and weak forces.

The strong force is the binding force that holds atomic nuclei together; conversely the weak force destabilises nuclei, causing a form of radioactivity that plays an essential role in the way that the sun produces its energy. As the years passed the belief grew that these four forces – electromagnetism, gravity, and the strong and weak forces – would be reunited in a Theory of Everything.

With the exception of general relativity, physicists have been able to ‘quantize’ the other three forces, since quantum mechanics deals with the atomic and sub-atomic domain. In effect they managed to get three trains running on the same size track. The quantum gravity train is still stuck at the station. In *The Infinity Puzzle* Oxford particle physicist Frank Close tells the tale of quantum field theory – the attempts to understand and then unite electromagnetism and the strong and weak forces.

In the 1930s the union of Maxwell’s theo-ry of electromagnetism, Einstein’s theory of special relativity, and quantum mechanics gave birth to a theory of the electromagnetic force known as quantum electrodynamics, or QED. However, in the bowels of the theory lurked a monster – infinity. The equations of QED kept predicting that the chance of some things occurring was ‘infinite’. When infinity pops up in physics it spells disaster since, as Close explains, it is ‘proof that you are trying to apply a theory beyond its realm of applicability’. In the case of QED, if you can’t calculate something as basic as a photon – a particle of light –

interacting with an electron without getting infinity, you haven’t got a theory.

It was the late 1940s before a way was found to solve the infinity puzzle in QED by a process called renormalisation. The calculations of many properties of atoms and their constituent particles, including those for the mass and charge of an electron, gave infinity as the answer. However, these two quantities of the electron had already been measured to a high degree of precision using other methods and the results were sufficient to provide benchmarks for anything else physicists wished to compute in QED. Instead of infinity, many of the answers now turned out to be finite and correct. Some physical quantities that have been calculated using renormalisation agree with earlier experiments to an accuracy of one part in a trillion, which is an order of magnitude akin to the diameter of a hair when compared to the width of the Atlantic.

Renormalisation may have been inelegant but its ‘recipe for extracting sensible answers for QED worked’. Those who cooked it up independently of each other – Richard Feynman, Julian Schwinger and Sin-Itiro Tomonaga – won a share of the 1965 Nobel Prize in Physics.

When it came to the weak force, infinity was not so easy to banish, even with the efforts of the world’s leading physicists over a quarter of a century. It was the brilliant Dutch postgraduate student Gerard ’t Hooft who finally found a solution. The nature of the problem, how it was solved, and the inevitable jostling for Nobel Prizes are major themes of Close’s gripping and extensively researched narrative history of particle physics over the last sixty years.

It may be a collective enterprise but, as Close’s book reveals, science is full of wrong turns, partial answers, missed opportunities and misunderstandings. How could it be otherwise, since the dispassionate, logic-driven stereotype of the scientist is a fiction? The physicists in *The* *Infinity Puzzle* ‘experience the same emotions, pressures and temptations as any other group of people, and respond in as many ways’.

A timeline of who did what when, together with a glossary, could be added to the paperback, to help readers as they grapple with gauge invariance, parity violation, spontaneous symmetry breaking, gluons, colour, the Higgs boson and SU(2)xU(1). Yet Close has succeeded in humanising a dramatic era of physics in what is my science book of the year. Some sections of his narrative are difficult because of the inherent nature of the ideas he’s trying to explain. But then, it took exceedingly clever people to devise them.

‘Hold Infinity in the palm of your hand,’ William Blake wrote in the ‘Aug-uries of Innocence’. Frank Close does a fabulous job of reconstructing how physicists like Feynman and ’t Hooft managed to do exactly that.

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